Question

Question
Use the image to answer the question.

An illustration shows rectangle extending to a triangle on the right. The top of the rectangle extends as the hypotenuse toward the bottom. The dimensions of the figure are as follows: the top is 8 centimeters, the left is 4 centimeters, and the bottom is 10 centimeters, including the side of the extended triangle.

What is the area of the figure in square centimeters?(1 point)

Answer 1

To find the area of the figure which consists of a rectangle combined with a right triangle, we can break it down into two parts: the area of the rectangle and the area of the triangle.

1. **Area of the Rectangle**:
The area \( A \) of a rectangle is calculated as:
\[
A = \text{length} \times \text{width}
\]
In this case, we have:
- Length (top side) = 8 cm
- Width (left side) = 4 cm

Therefore, the area of the rectangle is:
\[
A_{rectangle} = 8 \, \text{cm} \times 4 \, \text{cm} = 32 \, \text{cm}^2
\]

2. **Dimensions and Area of the Triangle**:
The triangle is right-angled at the bottom left corner, with:
- Base (bottom side of the triangle) = 10 cm
- Height (left side of the triangle) = 4 cm

The area \( A \) of a triangle is calculated as:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Hence, the area of the triangle will be:
\[
A_{triangle} = \frac{1}{2} \times 10 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 40 \, \text{cm}^2 = 20 \, \text{cm}^2
\]

3. **Total Area of the Figure**:
To get the total area of the figure, we add the area of the rectangle and the area of the triangle:
\[
A_{total} = A_{rectangle} + A_{triangle} = 32 \, \text{cm}^2 + 20 \, \text{cm}^2 = 52 \, \text{cm}^2
\]

Thus, the area of the figure is **52 square centimeters**.